Blind carrier frequency offset estimator based on single-OFDM-symbol PN ranging code in multi-user OFDMA uplink

ABSTRACT

A blind carrier frequency offset estimator is based on a single-OFDM-symbol training sequence in multi-user OFDMA uplink. Through multiple access interference modeling and analysis, a virtual user is employed that occupies the all null sub-carriers. By minimizing the energy leakage on the virtual user in term of tentative frequency offsets, the estimator can approach the real frequency offset. The estimator performs only on frequency-domain, simplifies interference calculations, and lowers the rank of the matrix. An iterative computation method is used to approach the real frequency offset.

RELATED APPLICATION

The present application claims priority of Chinese Application No.200610063945.3 filed Aug. 31, 2006, and is a continuation of, U.S.patent application Ser. No. 11/833,157 filed on Aug. 2, 2007. Thedisclosure of the foregoing United States patent application isspecifically incorporated herein by this reference in its entirety andassigned to STMicroelectronics (Beijing) R&D Company LTD., assignee ofthe present invention.

BACKGROUND OF THE INVENTION

The present invention relates to wireless transmission, and moreparticularly to a method for estimating a carrier frequency offset foran interleaved OFDMA uplink receiver.

As a widely used technique for high data rate wireless transmission, theOFDM (Orthogonal Frequency Division Multiplexing) technique makes use ofa set of overlapping but orthogonal sub-carriers to reach high spectrumefficiency. Inheriting from OFDM, OFDMA (orthogonal frequency divisionmultiple access) has been proposed in many broadband wireless systems toprovide more flexible wireless access scheme and to take more advantageof diversity gain by allocating a user a set of permutation-driveninterleaved sub-carriers that guarantee a large sub-carrier spacing foreach user.

Working in a mobile wireless environment, OFDMA is subject tosynchronization errors, such as the misalignments from the terminals tothe base-station, the discordances between the oscillator of thebase-station and those of the terminals, and Doppler shifts of theterminals. Like the OFDM technique, OFDMA is so sensitive to thesynchronization errors that a small frequency offset would lead to theloss of the orthogonality among the sub-carriers, and that a short timedelay would result in the complex exponential twiddle on thefrequency-domain.

The time-domain received signal in uplink is a multiplex of themulti-user signals that are subject to the different frequency offsets,time delays, and channel distortions. The interleaving topology of OFDMAdeteriorates this issue by turning the ICI (inter-channel-interference)among the sub-carriers to the MAI (multiple access interference) amongusers. Besides, synchronization errors start to fluctuate when a usermoves fast.

In order to keep the synchronization of terminals and base-station, aranging process is taken to detect the synchronization errors of aterminal and to control the adjustment of the terminal's transmission ina close loop between this terminal and the base-station.

Functionally, the ranging process is classified into initial ranging andperiodic ranging. Initial ranging takes place when a terminal is(re-)registered into the network; while periodic ranging is performed tokeep the synchronization between a terminal and the base-station duringits constant transmission. Usually, the initial ranging consumes moresignaling resources by transmitting multiple OFDM symbols trainingsequence in uplink by which the base-station receiver is able toestimate the synchronization errors accurately but in relative long timeinterval; and the periodic ranging needs single OFDM symbol trainingsequence in uplink by which the base-station receiver can estimate thesynchronization errors in a short time interval.

The synchronization errors of a low mobile or even fixed terminal maychange so slowly that after the initial ranging reduces thesynchronization errors of the terminal under an acceptable criterion,the base-station hardly performs any periodic ranging for itsmaintenance. But, once the terminal speeds up, its synchronizationerrors may fluctuate dramatically so as to require frequent periodicranging processes. Among the synchronization errors, frequency offset isthe most important one, for it would destroy the orthogonality causingMAI. (The phase rotations resulting from the time delays can be, more orless, compensated by the channel estimator.)

In conventional OFDM system uplink, a common pre-defined trainingsequence (ranging code) is transmitted on the overall sub-carrier in oneOFDM symbol. And with a repetitious structure on the time-domain, thistraining sequence can be taken by ML (maximum likelihood) algorithm toestimate the frequency offset. However, this kind of ranging codedoesn't work in OFDMA uplink, because 1) the ranging code by no meansoccupies the overall band; and 2) it isn't a common pre-defined trainingsequence but a CDMA (code division multiplex access) code generated byPN (pseudo-noise) polynomial in order to distinct terminals.

An alternative to estimate the frequency offset in OFDMA uplink is torepeatedly transmit a CDMA ranging code in multiple consecutive OFDMsymbols (on the partial band) with phase continuity on the time-domain.Then, the base-station receiver can still apply ML to the repetitioustraining sequence. This method is taken in the initial ranging.

IEEE802.16e OFDMA system adopts initial ranging and periodic ranging.FIG. 1 shows the mandatory initial ranging and periodic ranging.

FIG. 1( a) is the time-domain illusion 100 of the initial-rangingtransmission. The initial-ranging transmission is performed during twoconsecutive OFDM symbol periods 102 and 104 with copies of specificduration of last samples as CP 106.

FIG. 1 (b) is the time-domain illusion 110 of the periodic rangingtransmission. The periodic ranging transmission is performed during oneOFDM symbol period 112 with a copy of specific duration of last samplesas CP.

These repetitions of symbol period, termed CP, provide multipathimmunity as well as tolerance for symbol time synchronization errors.

Initial ranging serves registering a new terminal into network. The timedelays, frequency offsets, and transmission power of an un-registeredterminal shall be estimated and adjusted to guarantee its on-goingreliable transmission. A base-station grants an initial rangingopportunity by allocating ranging channels in an uplink sub-frame. Thegrant information is encapsulated into a UL_MAP that is broadcast in thedownlink sub-frame. Given a ranging opportunity, terminals collide onthese ranging channels by transmitting a CDMA code, denoted as aninitial ranging code, which is randomly selected from a CDMA codecandidate set specified by the base-station. This ranging code will bedetected and transmitted together with the parameter adjustment messagein a ranging response during the next downlink opportunity to notify theterminal to be adjusted.

Periodic ranging serves re-synchronizing a terminal with thebase-station. A base-station grants a periodic ranging opportunity in anuplink sub-frame. The terminals collide on the ranging channel bytransmitting a CDMA code that is randomly selected from a candidate setspecified by the base-station.

A prior art solution has been proposed by Young-Ha Lee et al. Thissolution is applied to solve synchronization of an uplink between asubscriber station and a base-station by utilizing the ranging system ina multiple access wireless communication system of OFDMA.

However, this solution is only restricted to timing synchronizationrather than frequency synchronization. Since OFDMA system is verysensitive to frequency synchronization errors in a mobile environment,performing the synchronization process without considering frequencyoffset becomes inapplicable in practice.

Another prior art solution has been proposed by Chang-Wahn Yu et al.This solution is applied to process the ranging channels to measure thepropagation delay and the power of each subscriber station.

In an OFDMA system, each subscriber station has different carrierfrequency offsets if the system is not synchronized. The orthogonalityamong these subcarriers of the different subscriber stations are thusdestroyed due to MAI. Therefore, the insufficiencies of the abovesolution are that this solution does not take into account of frequencyoffset either.

A challenge to the periodic ranging is how to estimate the CFO based ona single-OFDM-symbol CDMA ranging code, when it comes to a mobileenvironment.

SUMMARY OF THE INVENTION

According to the present invention, a method for blind carrier frequencyoffset estimator is based on a single-OFDM-symbol training sequence inmulti-user OFDMA uplink. Through multiple access interference modelingand analysis, a virtual user is employed that occupies all nullsub-carriers. By minimizing the energy leakage on the virtual user interm of tentative frequency offsets, the method of the present inventioncan approach the real frequency offset. Besides, the method of thepresent invention is performed only in the frequency-domain, simplifiesinterference calculations, and lowers the rank of the matrix. Finally,an iterative computation method is used to approach the real frequencyoffset.

According to the present invention, a frequency offset estimation methodfor interleaved OFDMA uplink estimates frequency offset based on a oneOFDM symbol (on the partial band) CDMA training sequence, is a blindestimation, i.e. without knowing the transmitted CDMA ranging code, andis a low complexity method. The method of the present invention has theadvantage that it is performed only on the frequency-domain. The signalsdo not need to be transformed to the time-domain as is done withconventional CFO estimators. The method of the present invention has theadditional advantage of being a low complexity and memory saving method,because the introduction of an influence factor for MAI modeling greatlyreduces the rank of the correction matrix.

BRIEF DESCRIPTION OF THE DRAWINGS

The aforementioned and other features and objects of the presentinvention and the manner of attaining them will become more apparent andthe invention itself will be best understood by reference to thefollowing description of a preferred embodiment taken in conjunctionwith the accompanying drawings, wherein:

FIG. 1( a) is a diagram of an initial ranging method;

FIG. 1( b) is a diagram of a periodic ranging method according to theprior art;

FIG. 2 is a diagram of a single-user signal model according to thepresent invention;

FIG. 3 is a multi-user signal model according to the present invention;

FIG. 4 is a plot of the cost function vs. the tentative CFO according tothe present invention;

FIG. 5 is a flow chart of an iterative computational method according tothe present invention; and

FIG. 6 is a diagram of an OFDMA system incorporating the method of thepresent invention.

DESCRIPTION OF THE INVENTION

Prior to the introduction of the CFO estimator, we shall develop abase-band signal model for the interleaving OFDMA uplink. Starting byconstructing a single-user signal model, we will deduce a multi-usersignal model with CFO and a time-variant frequency-selective channel.

An equivalent base-band single-user transmitter/receiver 200 isillustrated in FIG. 2. FIG. 2 illustrates a single-user base-band signalmodel of an interleaving OFDMA system. The out-modem part of thetransmitter, such as randomization, channel coding, etc, is simplifiedas a modulator 202, and the receiver part is simplified as ade-modulator 204 respectively. The OFDM Framing/DeFraming block 206, 208is used for constructing/deconstructing the standard compatible OFDMAtransmission frame. Also the IFFT transformation 210 converts thefrequency-domain signal into time-domain and the CP is appended 212 toeach OFDM symbol after IFFT transformation 210. On the receiver side,FFT transformation 214 and CP removal block 216 are implemented forinverse operation as a transmitter part.

Focusing on frequency offset estimation, we can safely simplify theouter-modem part of the transmitter as a (de-)modulator. Definecomplex-valued vector S_(M×1)=[s(0), s(1), s(2), . . . , s(M−1)]^(T) asthe signals from the modulator to be transmitted in one OFDM symbol.Then, the M signals are to be mapped onto one frequency-domain OFDMsymbol vector (a complex vector of length of N×1) by a set ofpre-defined index. The remaining (N−M) entries are set to be zeros. Themapping relationship can be realized by a position index (sc(0), sc(1),sc(M−1)), that is, s(i) is mapped at the sc(i)-th entries of thefrequency-domain OFDM symbol vector. Define a position matrixP_(N×M)=[ε_(sc(0)), ε_(sc(1)), . . . , ε_(sc(M−1))], where ε_(j) is(N×1) zeros vector but with its j-th entry being 1. Thus, thefrequency-domain OFDM symbol signal can be expressed as P·S. IFFToperation can be realized by left-multiplication of a (N×N) IFFT matrixW^(H). The (k,l) entry of W is defined as

$N^{\frac{1}{2}} \cdot {{\mathbb{e}}^{{- j}\frac{2{\pi \cdot k \cdot l}}{N}}.}$The CP (cyclic prefix) operation is also represented by a leftmultiplication of the matrixCP_((Ncp+N)×N)=[[O_(Ncp×(N−Ncp))I_(Ncp×Ncp)]^(T)I_(N×N)]^(T), whereN_(cp) is length of CP. Finally, the transmitted signal vectorX_((N+Ncp)×1) is:X _((N+N) _(CP) _()×1) =CP _((N) _(CP) _(+N))×N·W _(N×N) ^(H) P _(N×M)·S _(M×1)  Equation 1The signal vector X is sequentially transmitted through a time-varyingfrequency selective channel. This continuous channel distortion can bemodeled as:

$\begin{matrix}\begin{matrix}{{y(t)} = {{{\mathbb{e}}^{{j2\pi}\; F_{0}t} \cdot {{h\left( {\tau,t} \right)} \otimes {x(t)}}} + {n(t)}}} \\{= {{{\mathbb{e}}^{{j2\pi}\; F_{0}t}{\int_{0}^{\,^{\tau}\max}{{h\left( {\tau,t} \right)}{x\left( {t - \tau} \right)}\ {\mathbb{d}\tau}}}} + {n(t)}}}\end{matrix} & {{Equation}\mspace{14mu} 2}\end{matrix}$where h(τ,t) is channel impulse response simplified to h(τ) during oneOFDM symbol; F₀ is CFO; n(t) is AWGN noise; τ_(max) is the maximumexcess delay. Discrete-time equivalent of Equation 2 by replacing t withi/F_(s), (F_(s) is the sampling frequency), is:

$\begin{matrix}{{y(i)} = {{{\mathbb{e}}^{{j2\pi}\; f_{0}i}{\sum\limits_{l = 0}^{N_{\max} - 1}{{h(l)}{x\left( {i - l} \right)}}}} + {n(i)}}} & {{Equation}\mspace{14mu} 3}\end{matrix}$where N_(max)=T_(max)·F_(s), f₀=F₀/F_(s) is the normalized CFO. IfN_(max)<N_(CP), no ISI (inter-symbol-interference) occurs, so thereceived time-domain signal vector is:Y _(N×1) =e ^(j2πf) ⁰ ^(·N) ^(CP) ·diag(g(f ₀))_(N×N) ·W _(N×N) ^(H) ·P_(N×M)·diag(h)_(M×M) ·S _(M×1)  Equation 4where g(f)=[e^(j2π·f·0), e^(j2π·f·1), . . . , e^(j2π·f·(N−1))], andh=[H(sc(0)), H(sc(1)), . . . , H(sc(M−1))] (H(i) is designated for thechannel frequency response at the i-th sub-carrier). The receivedfrequency-domain signal can be expressed by left multiplications of aFFT matrix W and position matrix P^(T):R _(M×1) =e ^(j2πf) ⁰ ^(N) ^(CP) P ^(T) ·W·diag(g(f ₀))·W ^(H)·P·diag(h)·S _(M×1)  Equation 5Equation 5 is the base-band signal transmission model of the inner-modempart. If f₀=0, i.e. no CFO presents, because the matrixdiag(g(f₀))=I_(N×N). And with W·W^(H)=I_(N×N) and P^(T)·P=I_(M×M), wecan rewrite R:R _(M×1) =e ^(j2πf) ⁰ ^(N) ^(CP) ·diag(h)·S _(M×1)  Equation 6Apparently, f₀=0 gives rise to no interference between sub-carriers.

An equivalent base-band multi-user transmitter/receiver 300 isillustrated in FIG. 3. FIG. 3 illustrates a multi-user based band signalmodel for an interleaving OFDMA system. The out-modem part oftransmitter, such as randomization, channel coding, etc, is simplifiedas a modulator 302, and the receiver part is simplified as ade-modulator 304, respectively. The OFDM Framing/DeFraming block 306,308 is used for constructing/deconstructing the standard compatibleOFDMA transmission frame. Also, the IFFT transformation 310 converts thefrequency-domain signal into time-domain and the CP is appended 312 toeach OFDM symbol after IFFT transformation 310. On the receiver side,FFT transformation 314 and CP removal block 316 are implemented forinverse operation as a transmitter part.

Comparing with the single user model, the user De-Mux block 318 isimplemented on the receiver side to extract each single user data fromits location within the OFDMA transmission frame.

In order to give out a multi-user signal model, we denote thesuperscript (•)^((k)) as the assignment to the k-th user. Since one OFDMsymbol is shared by several users without collision (overlapping), wehave:

$\begin{matrix}{{\left( P^{(k)} \right)^{T} \cdot \left( P^{(l)} \right)} = \left\{ \begin{matrix}I_{M^{(k)} \times M^{(l)}} & {k = l} \\O_{M^{(k)} \times M^{(l)}} & {k \neq l}\end{matrix} \right.} & {{Equation}\mspace{14mu} 7}\end{matrix}$And

${\sum\limits_{k = 0}^{N_{user} - 1}M^{(k)}} \leq {N - N_{left\_ guard} - {N_{{right\_ guard}.}.}}$Thus, the received time-domain signal can be a sum of those ofindividual users:

$\begin{matrix}\begin{matrix}{Y_{N \times 1} = {\sum\limits_{k = 0}^{N_{user} - 1}Y_{N \times 1}^{(k)}}} \\{= {\sum\limits_{k = 0}^{N_{user} - 1}{{\mathbb{e}}^{{j2\pi}\; f_{0}^{(k)}N_{CP}} \cdot {{diag}\left( {g\left( f_{0}^{(k)} \right)} \right)} \cdot}}} \\{W^{H} \cdot P^{(k)} \cdot {{diag}\left( h^{(k)} \right)} \cdot S^{(k)}}\end{matrix} & {{Equation}\mspace{14mu} 8}\end{matrix}$Similarly, the received frequency-domain of the k-th user is:

$\begin{matrix}{R_{M^{(k)} \times 1}^{(k)} = {{{{\mathbb{e}}^{{j2\pi}\; f_{0}^{(k)}N_{CP}}\left( P^{(k)} \right)}^{T} \cdot W \cdot {{diag}\left( {g\left( f_{0}^{(k)} \right)} \right)} \cdot W^{H} \cdot P^{(k)} \cdot {{diag}\left( h^{(k)} \right)} \cdot S_{M^{(k)} \times 1}^{(k)}} + {\sum\limits_{\underset{l \neq k}{{l = 0},}}^{N_{user} - 1}{{{\mathbb{e}}^{{j2\pi}\; f_{0}^{(l)}N_{CP}}\left( P^{(k)} \right)}^{T} \cdot W \cdot {{diag}\left( {g\left( f_{0}^{(l)} \right)} \right)} \cdot W^{H} \cdot P^{(l)} \cdot {{diag}\left( h^{(l)} \right)} \cdot S_{M^{(l)} \times 1}^{(l)}}}}} & {{Equation}\mspace{14mu} 9}\end{matrix}$The first term on the right-hand side of Equation 9 is the receivedsignal from the k-th user. If f₀ ^((k))≠0, the sub-carrier interferencepresents, denoted as self-interference. The second term on theright-hand side of Equation 9 includes the signals from the other users.If f₀ ^((l))=0, ∀l, l≠k, the sum of the second term is zero because ofEquation 7; otherwise, it introduces the interference from other users,denoted as MAI.

In order to design a blind CFO estimator, we shall introduce a conceptof a “virtual user”. As its name suggests, UL PUSC of IEEE802.16esystem, one of the mandatory transmission structure, uses some of thesub-channels, that is, some sub-channels are deliberately set to zeros.These null sub-channels are uniformly distributed on the overall band ina given permutation way to separate different users. In a practicalsystem, about 60%˜75% sub-channels are used, while the remainders arenull sub-channels against the MAI. Thus, despite the presence of theinterferences due to the existing CFOs, their influence from one user onanother user would greatly diminish along with the increasing of thesub-carrier distances between the two users.

Another issue is sectorization. Like other cellular systems, IEEE802.16esystem sectorizes its cell. All of the available sub-channels, excludingthe null sub-channels, are grouped into three segments. Each segment isassigned to a sector's usage. Concurrently, three sets of directionaltransmitter/receiver antenna arrays are installed at the BS for thesectors. Therefore, in a given sector, the signal energies (orinterferences) from the neighboring sectors can be low enough to beconsidered as white noise. Accordingly, the sub-channels of the othersegments can be regarded as null sub-channels too.

Taking into account the two points above, there are a number of nullsub-channels in OFDMA uplink. These null sub-channels can be regarded asa special user that transmits only zero signals without CFO. We denotethis null sub-channel set as “virtual user.” Logically, it contributesno interferences on the other users; whereas the other users presentinterferences on it. Equation 10 expresses this relationship:

$\begin{matrix}{R_{M^{({null})} \times 1}^{({null})} = {N_{M^{({null})} \times 1} + {\sum\limits_{{l = 0},}^{N_{user} - 1}{\left( P^{({null})} \right)^{T} \cdot W \cdot {{diag}\left( {g\left( f_{0}^{(l)} \right)} \right)} \cdot W^{H} \cdot P^{(l)} \cdot {{diag}\left( h^{(l)} \right)} \cdot S_{M^{(l)} \times 1}^{(l)}}}}} & {{Equation}\mspace{14mu} 10}\end{matrix}$where the superscript (•)^((null)) is designated for the assignment tothe virtual user. The mapping relationship of the virtual user can berealized by a position index (null(0), null(1), . . . ,null(M^((null))−1)). And a null position matrix P_(N×M)=[ε_(null(0)),ε_(null(1)), . . . , ε_(null(M−1))].

In an ideal synchronous system, i.e., ω₀ ^((l))=0, ∀l, the virtual useronly transmits the white noise; otherwise, the MAI from other usersleaks on the virtual user's band. We name this MAI as “signal energyleakage.”

Due to the fact that CFO gives rise to the signal energy leakage thataugments the signal energy on the virtual user's band, we design a CFOestimator that minimizes the energy.

Ranging can be regarded as a specific user. Denote the superscript(•)^((ranging)) as the assignment to the ranging user. Define a jointposition index of the virtual user and the ranging user as((null+ranging)(0), (null+ranging)(1), . . . ,(null+ranging)(M^((null))+M^((ranging))−1))=(null(0), null(1), . . . ,null(M^((null))−1))∪(sc^((ranging))(0), sc^((ranging))(1), . . . ,sc^((ranging))(M^((ranging))−1)). The joint position matrix of thevirtual user and the ranging user is:P _(N×(M) _((null)) _(+M) _((ranging)) ₎^((null+ranging))=└ε_((null+ranging)(0)),ε_((null+ranging)(1)), . . .,ε_((null+ranging)(M) _((null)) _(+M) _((ranging)) ⁻¹⁾┘  Equation 11The observed frequency-domain joint signal of the virtual user and theranging user is:

$\begin{matrix}{R_{{({M^{({nll})} + M^{({ranging})}})} \times 1}^{({{null} + {ranging}})} = {{{{\mathbb{e}}^{{j2\pi}\; f_{0}^{({ranging})}N_{CP}}\left( P^{({{null} + {ranging}})} \right)}^{T} \cdot W \cdot {{diag}\left( {g\left( f_{0}^{({ranging})} \right)} \right)} \cdot W^{H} \cdot P^{({ranging})} \cdot {{diag}\left( h^{({ranging})} \right)} \cdot S_{M^{({ranging})} \times 1}^{({ranging})}} + {\sum\limits_{\underset{l \neq {ranging}}{{l = 0},}}^{N_{user} - 1}{{{\mathbb{e}}^{{j2\pi}\; f_{0}^{(l)}N_{CP}}\left( P^{({{null} + k})} \right)}^{T} \cdot W \cdot {{diag}\left( {g\left( f_{0}^{(l)} \right)} \right)} \cdot W^{H} \cdot P^{(I)} \cdot {{diag}\left( h^{(l)} \right)} \cdot S_{M^{(l)} \times 1}^{(l)}}}}} & {{Equation}\mspace{14mu} 12}\end{matrix}$Assuming that the other users have already been synchronized with theBS, that is, f₀ ^((l))=0, ∀l, l≠k, the second term of the right handside of Equation 12 turns to zeros:R _((M) _((null)) _(+M) _((ranging)) _()×1) ^((null+ranging)) =e ^(j2πf)⁰ ^((ranging)) ^(N) ^(CP) (P ^((null+ranging)))^(T) ·W·diag(g(f ₀^((ranging))))·W ^(H) ·P ^((ranging))·diag(h ^((ranging)))·S _(M)_((ranging)) _(×1) ^((ranging))  Equation 13Multiple R^((null+ranging)) by correction matrixes in term of atentative CFO f^((ranging)) and extract the signal of the virtual user:R′ _(M) _((nll)) _(×1) ^((null))=(P ^((null)))^(T) ·W·diag(g(f^((ranging))))·W ^(H) ·P ^((ranging+null)) ·R ^((nll+ranging))  Equation14Replace Equation 13 into Equation 14:R′ _(M) _((nll)) _(×1) ^((null)) =e ^(j2πf) ⁰ ^((ranging)) ^(N) ^(CP)·(P ^((null)))^(T) ·W·diag(g(f ^((ranging)) +f ₀ ^((ranging))))·W ^(H)·P ^((ranging))·diag(h ^((ranging)))·S _(M) _((ranging)) _(×1)^((ranging))  Equation 15Equation 15 indicates that R′^((null)) is the signal leakage from theranging user that is corrected by a tentative CFO f^((ranging)). Definea correct matrixC^((ranging))(f)=(P^((null)))^(T)·W·diag(g(f^((ranging))))·W^(H)·P^((null+ranging)).We re-write (14):R′ _(M) _((nll)) _(×1) ^((null)) =C ^((ranging))(f)·R^((nll+ranging))  Equation 16We can introduce a cost function in terms of the signal energy ofR′^((null)):J ^((ranging))(f)=(R′ _(M) _((nll)) _(×1) ^((null)))^(H) ·R′ _(M)_((nll)) _(×1) ^((null))=(R ^((null+ranging)))^(H)·(C^((ranging))(f))^(H) ·C ^((ranging))(f)·R ^((null+ranging))  Equation 17To explain why the estimated CFO minimizes the cost functionJ^((ranging))(f), we note that in Equation 15 f^((ranging))+f₀^((ranging))=0 leads to diag(g(f^((ranging))+f₀ ^((ranging))))=I_(N×N),i.e. R′^((null))=0. Thus, relying on the cost function, CFO estimator isgiven by:

${{\overset{\Cap}{f}}_{0}^{({ranging})} = {\underset{f}{\arg\;\min}{J^{({ranging})}(f)}}}\;$FIG. 4 shows the cost function in terms of tentative CFO.

As noted above, the CFO estimator is based on signal energy detection onthe virtual user. However, the generation of the correction matrixC^((ranging))(f) is high complex operation to be performed oncef^((ranging)) is updated. To address the simplification of the CFOestimator, we start by analyzing MAI property in OFDMA uplink.

From Equation 9, the interference from the l-th user on the k-th userdue to the CFO of the l-th user can be modeled as:MAI(k,l,f _(o) ^((l)))=e ^(j2πf) ⁰ ^((l)) ^(N) ^(CP) (P ^((k)))^(T)·W·diag(g(f ₀ ^((l))))·W ^(H) ·P ^((l)) ·R _(M) _((l)) _(×1)^((l))  Equation 18Define a MAI function m(k,l,f)=(P^((k)))^(T)·W·diag(g(f))·W^(H)·P^((l)),so the interference is re-written as:MAI(k,l,f ₀ ^((l)))=e ^(j2πf) ⁰ ^((l)) ^(N) ^(CP) ·m(k,l,f ₀ ^((l)))·R_(M) _((l)) _(×1) ^((l))  Equation 19To investigate the MAI property, we discard the term e^(j2πf) ⁰ ^((l))^(N) ^(CP) , for it only causes the phase rotation. Without loss ofgenerality, we can investigate MAI property by studying m(k,l,f). Thefunction m(k,l,f) returns a M^((k))×M^((l)) matrix, the (u,v) entry ofwhich is

${I\left( {u,v} \right)} = {\left( {1/N} \right) \cdot {\sum\limits_{n = 0}^{N - 1}{{\mathbb{e}}^{{{j2\pi}{({f + {{sc}^{(l)}{(u)}} - {{sc}^{(k)}{(v)}}})}}{n/N}}.}}}$It equals:

$\begin{matrix}{{I\left( {u,v} \right)} = {\frac{\sin\;{\pi\left( {f + {{sc}^{(l)}(u)} - {{sc}^{(k)}(v)}} \right)}}{N\;\sin\frac{\pi}{N}\left( {f + {{sc}^{(l)}(u)} - {{sc}^{(k)}(v)}} \right)} \cdot {\mathbb{e}}^{{- {{j\pi}{({1 - \frac{1}{N}})}}}{({f + {{sc}^{(l)}{(u)}} - {{sc}^{(k)}{(v)}}})}}}} & {{Equation}\mspace{14mu} 20}\end{matrix}$Noting that for a large N:

$\begin{matrix}{{\lim\limits_{N\rightarrow\infty}\frac{\sin\;{\pi\left( {f + {{sc}^{(l)}(u)} - {{sc}^{(k)}(v)}} \right)}}{N\;\sin\frac{\pi}{N}\left( {f + {{sc}^{(l)}(u)} - {{sc}^{(k)}(v)}} \right)}} = {\sin\;{c\left( {f + {{sc}^{(l)}(u)} - {{sc}^{(k)}(v)}} \right)}}} & {{Equation}\mspace{14mu} 21}\end{matrix}$the normalized power of l(u,v) decreases dynamically with the increaseof the distance |sc^((l))(u)−sc^((k))(v)| (it is an integer) fordifferent f (f≠0). It can be concluded that the interference from theu-th sub-carrier of the l-th user has the influence only on its limitedneighboring sub-carriers. In the case of f=0,sinc(sc^((l))(u)−sc^((k))(v))≡0 if and only if|sc^((l))(u)−sc^((k))(v)|≠0.We introduce an interference influence factor d to express the“effective” interference limitation:

$\begin{matrix}{{I\left( {u,v} \right)} = \left\{ \begin{matrix}{\sin\;{{c\left( {f + {{sc}^{(l)}(u)} - {{sc}^{(k)}(v)}} \right)} \cdot {\mathbb{e}}^{{- {{j\pi}{({1 - \frac{1}{N}})}}}{({f + {{sc}^{(l)}{(u)}} - {{sc}^{(k)}{(v)}}})}}}} & {{{{{sc}^{(l)}(u)} - {{sc}^{(k)}(v)}}} \leq d} \\0 & {else}\end{matrix} \right.} & {{Equation}\mspace{14mu} 22}\end{matrix}$With Equation 22, we can lower the rank of the correction matrixC^((ranging))(f) by discarding those null sub-carriers from which thedistances to the nearest ranging sub-carriers are greater than apre-defined distance d. Re-define null sub-carrier position index:{sc ^((null′))(l)εnull∥sc ^((null))(l)−sc ^((ranging))(m)|≦d,m=0,1, . .. M ^((ranging))}And the (u,v) entry of C^((ranging))(f) is l(u,v) in Equation 22 wheresc^((l))(u)=sc^((null′))(u), sc^((k))(v)=sc^((ranging)), andf=f^((ranging)).The cost function of J^((ranging))(f) is illustrated in FIG. 5. Knowingthat f₀ ^((ranging))ε(f₁,f₂), we can use iterative computation to reachthe estimated f^((ranging)):

-   -   1. f^((ranging))=f₁, J₀=+∞; (step 502))    -   2. Calculate C^((ranging))(f^((ranging))) with Equation 22;        (step 504)    -   3. Calculate R′_(M) _((nll′)) _(×1) ^((null′)) based on Equation        16; (step 506)    -   4. From R′_(M) _((nll′)) _(×1) ^((null′)), calculate        J^((ranging))(f^((ranging))) with Equation 17, and        J₁=J^((ranging))(f^((ranging))); (step 518)    -   5. if J₁>J₀, go to end and return f^((ranging)); (decision 508)    -   6. f^((ranging))=f^((ranging))+Δf_(step), if f^((ranging))>f₂,        go to end and estimate failure, otherwise J₀=J₁ and go to step        2; (steps 510, 512, and 516)    -   7. End.

The flow chart of the iterative method of the present invention is shownin FIG. 5. The flow chart of FIG. 5 also includes step 518. Step 518denotes J as J1 for the next step comparison and iteration. The flowchart also includes decision diamond 514 that ends the method of thepresent invention if the upper end of the carrier frequency offset isreached. The iterative method of the present invention can be enhancedif desired. For instance, Δf_(step) can be adjusted according theΔJ=J₁−J₀; a LMS (least Mean Square) algorithm can also be proposed toimprove better tracking performance.

The minimum value of the cost function is determined during theiterative method of the present invention, as is shown in FIG. 4. Forthe first time iteration, it is impossible for J1 to be greater than J0(positive infinity), and in step 512 J1 is denoted as J0, so for thenext step, the new frequency resulted cost function value is comparedwith J0, which has the same value of J1 (not positive infinity). Bysuccessive iterations, the method of the present invention is continueduntil the minimum value of cost function is found.

Referring now to FIG. 6, an entire OFDMA system 600 is shown, includingall of the blocks previously described. In addition, system 600 includesa CFO estimator block 620 incorporating the method of the presentinvention as was previously described. In addition, system 600 includesa frequency offset corrector block 622, which compensates for thefrequency offset estimated by the CFO estimator block 620.

As is known in the art, the entire system 600, and blocks 620 and 622 inparticular, can be implemented in an integrated circuit using DSPtechnology to realize all of the various mathematical steps andtransformations in the method of the present invention.

While there have been described above the principles of the presentinvention in conjunction with specific components, circuitry and biastechniques, it is to be clearly understood that the foregoingdescription is made only by way of example and not as a limitation tothe scope of the invention. Particularly, it is recognized that theteachings of the foregoing disclosure will suggest other modificationsto those persons skilled in the relevant art. Such modifications mayinvolve other features which are already known per se and which may beused instead of or in addition to features already described herein.Although claims have been formulated in this application to particularcombinations of features, it should be understood that the scope of thedisclosure herein also includes any novel feature or any novelcombination of features disclosed either explicitly or implicitly or anygeneralization or modification thereof which would be apparent topersons skilled in the relevant art, whether or not such relates to thesame invention as presently claimed in any claim and whether or not itmitigates any or all of the same technical problems as confronted by thepresent invention. The applicants hereby reserve the right to formulatenew claims to such features and/or combinations of such features duringthe prosecution of the present application or of any further applicationderived therefrom.

The following Abbreviations used herein are listed in Table I: AWGNAdditive White Gaussian Noise BS Base Station CDMA Code DivisionMultiple Access CFO Carrier Frequency Offset CP Cyclic Prefix FFT FastFourier Transform ICI Inter-Channel-Interference IFFT Inverse FastFourier Transform LS Least Square ISI Inter Symbol Interference LMSLeast Mean Square MAI Multiple Access Interference ML Maximum LikelihoodOFDM Orthogonal Frequency Division Multiplexing OFDMA OrthogonalFrequency Division Multiple Access PN Pseudo Noise PUSC Partial Used SubChannel

The following Parameters are used herein in Table II: M number of theavailable sub-carriers N OFDM modulation size S^((k)) complex datavector of user k S_(c) ^((k)) position index of user k P position matrixε_(j) N × 1 zero vector but with its j-th entry being 1 CP cyclic prefixmatrix N_(cp) length of CP W^(H) IFFT matrix W FFT matrix X transmittedsignal vector h(τ, t) channel impulse response n(t) AWGN noise τ_(max)maximum excess delay F_(s) sampling frequency F₀ CFO f₀ normalized CFO,F₀/F_(s) Y received time-domain signal vector I identity matrixN_(left-guard) left virtual guard size N_(right-guard) right virtualguard size R received frequency-domain signal vector R′ correctedreceived frequency-domain signal vector C correction matrix J costfunction in term of the signal energy m(k, I.f) MAI function

We claim:
 1. A method for estimating carrier frequency offset of asubscriber station by a base station for an uplink in an OFDMAcommunication system comprising: selecting a set of null sub-channelsfrom among all null sub-channels of the OFDMA communication system;computing, in a signal processing device, signal energy leakage intosaid set of null sub-channels; calculating a cost function value usingthe computed value of the signal energy leakage; and adjusting saidcarrier frequency offset to minimize signal energy leakage into said setof null sub-channels; wherein calculating the cost function value andsaid adjusting said carrier frequency offset comprise: initializing acarrier frequency offset value to provide a carrier frequency offsetreference value; initializing the cost function value to provide a costfunction reference value; calculating a correction matrix; calculatingthe cost function value using at least said correction matrix; comparingsaid calculated cost function value with said cost function referencevalue and proceeding either, in the case that said calculated costfunction value is greater than said cost function reference value, byreturning said carrier frequency offset reference value as the estimatedcarrier frequency offset and terminating the method; or, in the casethat said calculated cost function value is equal to or less than saidcost function reference value, by setting said cost function referencevalue equal to said calculated cost function value and modifying saidcarrier frequency offset reference value; and repeating said calculatinga correction matrix, said calculating a cost function value, and saidcomparing until either said calculated cost function value is greaterthan said cost function reference value, or a range of frequencyadjustment is exceeded; and wherein said modifying said carrierfrequency offset reference value comprises using a least mean squaresmethod.
 2. The method of claim 1 wherein said set of null sub-channelsfurther comprises null sub-channels of other segments.
 3. The method ofclaim 1 further comprising: discarding from said set of nullsub-channels any null sub-channel having a frequency that is at adistance greater than a predefined distance from any frequency of anyranging sub-channel of the OFDMA communication system.
 4. The method ofclaim 1 wherein said cost function is calculated using the formula:J ^((ranging))(f)=(R _(M) _((null)) _(×1) ^(l(null)))^(H) ·R _(M)_((null)) _(×1) ^(l(null))=(R ^((null+ranging)))^(H)·(C^((ranging))(f))^(H) ·C ^((ranging))(f)·R ^((null+ranging)) wherein f isa frequency, J^((ranging)) is the cost function, C^((ranging)) is thecorrection matrix, H as a superscript, denotes the Hermitian transpose,R^((null+ranging)) is the received frequency domain signal vector fromthe null and ranging channels, R_(M) _((null)) _(×1) ^(l(null)) is thecorrected received frequency domain signal vector corresponding to thenull channels, and M^(null) is the number of null sub-channels.
 5. Themethod of claim 1 wherein the method is performed only in thefrequency-domain and does not use phase information.
 6. The method ofclaim 1 wherein the method is performed without knowing a transmittedCode Division Multiple Access (CDMA) ranging code.
 7. An OFDMA uplinkreceiver comprising a signal processing device and configurable toperform a method for estimating a carrier frequency offset, wherein saidmethod comprises: selecting a set of null sub-channels from among allnull sub-channels of the OFDMA communication system; computing, in saidsignal processing device, signal energy leakage into said set of nullsub-channels; calculating a cost function value using the computed valueof the signal energy leakage; and adjusting said carrier frequencyoffset to minimize signal energy leakage into said set of nullsub-channels; wherein calculating the cost function value and saidadjusting said carrier frequency offset comprise: initializing a carrierfrequency offset value to provide a carrier frequency offset referencevalue; initializing the cost function value to provide a cost functionreference value; calculating a correction matrix; calculating the costfunction value using at least said correction matrix; comparing saidcalculated cost function value with said cost function reference valueand proceeding either, in the case that said calculated cost functionvalue is greater than said cost function reference value, by returningsaid carrier frequency offset reference value as the estimated carrierfrequency offset and terminating the method; or, in the case that saidcalculated cost function value is equal to or less than said costfunction reference value, by setting said cost function reference valueequal to said calculated cost function value and modifying said carrierfrequency offset reference; and repeating said calculating a correctionmatrix, said calculating a cost function value, and said comparing untileither said calculated cost function value is greater than said costfunction reference value, or a range of frequency adjustment isexceeded; wherein said modifying said carrier frequency offset referencevalue comprises using a least mean squares method.
 8. The OFDMA uplinkreceiver of claim 7 wherein said method further comprises: discardingfrom said set of null sub-channels any null sub-channel having afrequency that is at a distance greater than a predefined distance fromany frequency of any ranging sub-channel of the OFDMA communicationsystem.
 9. The OFDMA uplink receiver of claim 7 wherein said method isperformed only in the frequency domain and does not employ phaseinformation.
 10. The receiver of claim 7 wherein said cost function iscalculated using the formula:J ^((ranging))(f)=(R _(M) _((null)) _(×1) ^(l(null)))^(H) ·R _(M)_((null)) _(×1) ^(l(null))=(R ^((null+ranging)))^(H)·(C^((ranging))(f))^(H) ·C ^((ranging))(f)·R ^((null+ranging)) wherein f isa frequency, J^((ranging)) is the cost function, C^((ranging)) is thecorrection matrix, H as a superscript, denotes the Hermitian transpose,R^((null+ranging)) is the received frequency domain signal vector fromthe null and ranging channels, R_(M) _((null)) _(×1) ^(l(null)) is thecorrected received frequency domain signal vector corresponding to thenull channels, and M^(null) is the number of null sub-channels.
 11. AnOFDMA communication system, comprising: a base station in communicationwith at least one subscriber station; wherein communications between thebase station and any subscriber stations use OFDMA signaling; andwherein the base station uses a method of estimating carrier frequencyoffset of a subscriber station during an uplink communication, themethod comprising: selecting a set of null sub-channels from among allnull sub-channels of the OFDMA communication system; discarding fromsaid set of sub-channels any null sub-channel having a frequency that isat a distance greater than a predefined distance from any frequency ofany ranging sub-channel of the OFDMA communication system; computingsignal energy leakage into said set of null sub-channels using a signalprocessing device; calculating a cost function value using the computedvalue of the signal energy leakage; and adjusting said carrier frequencyoffset to minimize signal energy leakage into said set of nullsub-channels; wherein said adjusting said carrier frequency offsetcomprises: initializing a carrier frequency offset value to provide acarrier frequency offset reference value; initializing a cost functionvalue to provide a cost function reference value; calculating acorrection matrix; calculating a cost function value using at least saidcorrection matrix; comparing said calculated cost function value withsaid cost function reference value and proceeding either, in the casethat said calculated cost function value is greater than said costfunction reference value by returning said carrier frequency offsetreference value as the estimated carrier frequency offset andterminating the method, or, in the case that said calculated costfunction value is equal to or less than said cost function referencevalue, by setting said cost function reference value equal to saidcalculated cost function value and modifying said carrier frequencyoffset reference value; and repeating said calculating a correctionmatrix, said calculating a cost function value, and said comparing untileither said calculated cost function value is greater than said costfunction reference value, or a range of frequency adjustment isexceeded; wherein said modifying said carrier frequency offset referencevalue comprises using a least mean squares method.
 12. The system ofclaim 11 wherein said set of sub-channels further comprises sub-channelsof other segments.
 13. The system of claim 11 wherein the method isperformed only in the frequency-domain and does not employ phaseinformation.
 14. The system of claim 11 wherein the method is performedwithout knowing a transmitted Code Division Multiple Access (CDMA)ranging code.
 15. The system of claim 11 wherein said cost function iscalculated using the formula:J ^((ranging))(f)=(R _(M) _((null)) _(×1) ^(l(null)))^(H) ·R _(M)_((null)) _(×1) ^(l(null))=(R ^((null+ranging)))^(H)·(C^((ranging))(f))^(H) ·C ^((ranging))(f)·R ^((null+ranging)) wherein f isa frequency, J^((ranging)) is the cost function, C^((ranging)) is thecorrection matrix, H as a superscript, denotes the Hermitian transpose,R^((null+ranging)) is the received frequency domain signal vector fromthe null and ranging channels, R_(M) _((null)) _(×1) ^(l(null)) is thecorrected received frequency domain signal vector corresponding to thenull channels, and M^(null) is the number of null sub-channels.